Reservoir computing is a computational framework suited for temporal/sequential data processing. It is derived from several recurrent neural network models, including echo state networks and liquid state machines. A reservoir computing system consists of a reservoir for mapping inputs into a high-dimensional space and a readout for pattern analysis from the high-dimensional states in the reservoir. The reservoir is fixed and only the readout is trained with a simple method such as linear regression and classification. Thus, the major advantage of reservoir computing compared to other recurrent neural networks is fast learning, resulting in low training cost. Another advantage is that the reservoir without adaptive updating is amenable to hardware implementation using a variety of physical systems, substrates, and devices. In fact, such physical reservoir computing has attracted increasing attention in diverse fields of research. The purpose of this review is to provide an overview of recent advances in physical reservoir computing by classifying them according to the type of the reservoir. We discuss the current issues and perspectives related to physical reservoir computing, in order to further expand its practical applications and develop next-generation machine learning systems.
Modern computation based on the von Neumann architecture is today a mature cutting-edge science. In the Von Neumann architecture, processing and memory units are implemented as separate blocks interchanging data intensively and continuously. This data transfer is responsible for a large part of the power consumption. The next generation computer technology is expected to solve problems at the exascale with 1018 calculations each second. Even though these future computers will be incredibly powerful, if they are based on von Neumann type architectures, they will consume between 20 and 30 megawatts of power and will not have intrinsic physically built-in capabilities to learn or deal with complex data as our brain does. These needs can be addressed by neuromorphic computing systems which are inspired by the biological concepts of the human brain. This new generation of computers has the potential to be used for the storage and processing of large amounts of digital information with much lower power consumption than conventional processors. Among their potential future applications, an important niche is moving the control from data centers to edge devices. The aim of this Roadmap is to present a snapshot of the present state of neuromorphic technology and provide an opinion on the challenges and opportunities that the future holds in the major areas of neuromorphic technology, namely materials, devices, neuromorphic circuits, neuromorphic algorithms, applications, and ethics. The Roadmap is a collection of perspectives where leading researchers in the neuromorphic community provide their own view about the current state and the future challenges for each research area. We hope that this Roadmap will be a useful resource by providing a concise yet comprehensive introduction to readers outside this field, for those who are just entering the field, as well as providing future perspectives for those who are well established in the neuromorphic computing community.
Many social, biological, and technological networks consist of a small number of highly connected components (hubs) and a very large number of loosely connected components (low-degree nodes). It has been commonly recognized that such heterogeneously connected networks are extremely vulnerable to the failure of hubs in terms of structural robustness of complex networks. However, little is known about dynamical robustness, which refers to the ability of a network to maintain its dynamical activity against local perturbations. Here we demonstrate that, in contrast to the structural fragility, the nonlinear dynamics of heterogeneously connected networks can be highly vulnerable to the failure of low-degree nodes. The crucial role of low-degree nodes results from dynamical processes where normal (active) units compensate for the failure of neighboring (inactive) units at the expense of a reduction in their own activity. Our finding highlights the significant difference between structural and dynamical robustness in complex networks.
Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on-and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.
A widely used complex-valued activation function for complex-valued multistate Hopfield networks is revealed to be essentially based on a multilevel step function. By replacing the multilevel step function with other multilevel characteristics, we present two alternative complex-valued activation functions. One is based on a multilevel sigmoid function, while the other on a characteristic of a multistate bifurcating neuron. Numerical experiments show that both modifications to the complex-valued activation function bring about improvements in network performance for a multistate associative memory. The advantage of the proposed networks over the complex-valued Hopfield networks with the multilevel step function is more outstanding when a complex-valued neuron represents a larger number of multivalued states. Further, the performance of the proposed networks in reconstructing noisy 256 gray-level images is demonstrated in comparison with other recent associative memories to clarify their advantages and disadvantages.
We study tolerance of dynamic behavior in networks of coupled heterogeneous oscillators to deterioration of the individual oscillator components. As the deterioration proceeds with reduction in dynamic behavior of the oscillators, an order parameter evaluating the level of global oscillation decreases and then vanishes at a certain critical point. We present a method to analytically derive a general formula for this critical point and an approximate formula for the order parameter in the vicinity of the critical point in networks of coupled Stuart-Landau oscillators. Using the critical point as a measure for dynamical robustness of oscillator networks, we show that the more heterogeneous the oscillator components are, the more robust the oscillatory behavior of the network is to the component deterioration. This property is confirmed also in networks of Morris-Lecar neuron models coupled through electrical synapses. Our approach could provide a useful framework for theoretically understanding the role of population heterogeneity in robustness of biological networks.
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